The skewed weak lensing likelihood: why biases arise, despite data and theory being sound

We derive the essentials of the skewed weak lensing likelihood via a simple Hierarchical Model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing analyses are naturally biased low, and this does not indicate any new physics such as deviations from $\mathrm{\Lambda }$CDM. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from CMB analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30 percent of the standard deviation per data point, dependent on the properties of the weak lensing survey. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses.